After 1938 Charles Herbert Brown moved next door to no. 24 Giffin Street - in 1946 Lily B. Brown appears with him.
So, I think you are going to have to purchase Lily's birth certificate to confirm exactly who her mother was and if Charles Herbert Brown was her father (perhaps he was some other relative that Lily lived with).
Looking at electoral rolls, births/marriages etc. this looks like the scenario (but only the birth certificate of Lily can confirm (or not):
I mentioned earlier that in 1923 a Martha Addis was living with Charles Herbert Brown at 22 Giffin St - I believe these 2 are Lily's parents, and that the mmn on Lily's birth should have read Errington!
A John Addis married a Martha Errington in Ruthin,Denbighshire in Sept.qtr.1915 and son Edward V. Addis was born Dec.qtr.1918 St Asaph, Merionethshire). A Blanche Addis, mmn Errington, birth Sept.1922 Greenwich - she also lived at 24 Giffin St. with Charles before she married in 1941.
However, having now found a tree on Ancestry, John Addis who married Martha Errington was actually a John William Addis and he was killed in WW1 on 7/7/1916 - wife Martha signed for his effects on 1/10/1919. That being said, there is no way that he was the father of Edward Victor (born 1918) and Blanche (born 1922). Edward Victor Addis himself (married in 1939 Surrey) was killed in 1944 (WW2), shown as the son of John William and Martha Addis!!!! The tree has no date of death for Martha which is no surprise since she'd left Wales and was in Deptford/Greenwich from at least 1922 until 1938.
So, with husband John Addis killed in 1916 have no idea who the father was of son Edward and daughter Blanche - with third child being Lily Beatrice Brown it seems pretty likely that Charles Herbert Brown and Mary Addis nee Errington were her parents as Martha lived with him as wife until 1938, Blanche lived with him as did Lily. Martha said to be born 1888 Liverpool so no idea what happened to her - cannot see the death of a Martha Addis/Brown bc.1888 around 1938 when she disappears from electoral rolls so don't know if she died or whether she just took off again leaving 2 of her 3 children with Charles. Possible marriage of Charles and Martha in 1928 Greenwich.
Martha Errington certainly seems to have led a colourful life.
Annette